Chapter 5 Applications
5.3 Optimization
5.3.4 Combined optimization
5.3 Optimization 69
Chapter 6
Conclusion and outlook
As an effective method, reciprocity principle has been widely used to solve structure and fluid problems in many fields. This study extend the application of reciprocity principle to the fluid-structure interaction problems with the finite element method. The reciprocity principle is first applied to the structure optimization of an airplane, then various evaluation procedures are in-vestigated for vibro-acoustic computations. Finally, the feasibility of an optimization procedure for reducing sound pressure levels using the reciprocity principle is proved by this study. The optimization can be performed not only for one single ear position, but also for the whole group of ear positions. One advantage of the usage of the reciprocity principle is, that, one can per-form the calculation even if the location of the load is not precisely defined.
To perform the panel participation factor, the cabin part of the fuselage is subdivided into one floor region, one wall region and two skin regions. The computation results show: In the low frequency range, the floor region plays the leading role while the partition wall is completely irrelevant. For high frequencies, on the other hand, all the structure parts are more or less sig-nificant.
After the weak points of the structure are found and modified by inserting tuned mass dampers, various methods such as determining the equivalent radiated power can be applied to evaluate the effect of the optimization. In Nastran, ERP provides an approximate value for the acoustic power radiated from the structure. And compare to the ACPOWER command, the computing time can be saved to a large extent by using ERP.
There is still room for improvement and further optimization. For example the number of tuned mass damper can be reduced through continuous optimization. Besides, a symmetric load can be employed so that some pressure peaks will disappear and the result is closer to reality, which also means less weight used for dampers.
Bibliography
[1] F. Ihlenburg,Computational Acoustics, lecture notes (2011)
[2] F. Ihlenburg,Finite Element Analysis of Acoustic Scattering, Springer-Verlag (1998) [3] K.J. Bathe,Finite Element Procedures, Prentice Hall (1996)
[4] F. Ihlenburg, Sound in Vibrating Cabins: Physical Effects, Mathematical Description, Computational Simulation with FEM2006
[5] Earl G. Williams,Fourier Acoustics: Sound Radiation and Nearfield Acoustical Hologra-phy, Academic Press (1999)
[6] MSC.Software Corporation, Dynamic Analysis User’s Guide (2011) [7] MSC.Software Corporation, Nastran Quick Reference Guide (2010)
[8] F. J. Fahy,Some Applications of the Reciprocity Principle in Experimental Vibroacoustics, 2002
[9] L. M. Lyamshev,A Question in Connection with the Principle of Reciprocity in Acoustics, 1959
[10] MSC.Software Corporation, Nastran Release Guide (2010)
[11] Wu Guangqiang, Sheng Yun, Fang Yuan, Coupled Acoustic-structural Finite Element Analysis of Vehicle Interior Noise Based on Acoustic Sensitivity, 2009
[12] Wang Jun, Ning Wei, Zhang Jinghui,Numerical Simulation of Reverberant Acoustic Field Adopting Reciprocity Theorem, 2010
[13] K. Wiechmann, J. Hiller, Evaluation and Visualization of Equivalent Radiated Power, 2011
[14] http://en.wikipedia.org/wiki/Helmholtz equation
[15] http://www.esm-gmbh.de/EN/Products/Tuned mass dampers
BIBLIOGRAPHY 72
[16] http://www.airliners.de/management/marketing/lufthansa-zeigt-neue-europa-kabine/22909
[17] http://www.pmi.lv/soft/stirel/index.htm
Appendix A
Nastran input file for SPL Response
$ MODAL FREQUENCY RESPONSE SOL 111
CEND
$
TITLE= FLUID-STRUCTURE-RESPONSE
SUBTITLE = Force Excitation structure 1N, Response Fluid, 20-200Hz LABEL = Modal 0-320HZ
ECHO = NONE
$
$ Measuring points for 42 ear positions
SET 1 = 747064,747148,749022,750134,750218,752246,753066,753150,755470, 755998,756082,757550,757634,758694,759078,760482,760566,762302,763304, 763421,765478,767316,767400,769114,770210,770294,772194,772982,773066, 775274,775754,775838,777306,777390,778354,778674,780078,780162,781754, 782740,782857,784794
$ fluid response output
DISPLACEMENT(PLOT,SORT1,REAL,PUNCH)=1
$
METHOD(STRUCT) = 50 METHOD(FLUID) = 51 FREQ = 200
DLOAD = 2000
$
BEGIN BULK
$
$ Fluid and Structure meshes include ’FEM_all_coupled.bdf’
$ Absorbing boundary meshes include ’CAABSF.bdf’
$
$1...2...3...4...5...6...7...8...9...
PARAM AUTOSPC YES
74
PARAM POST -1
$
$ ABSORBING BOUNDARY CONDITIONS
$1...2...3...4...5...6...7...8...9...
PAABSF 10 210.8 210.8
$ DYNAMIC LOADING ON STRUCTURE
$1...2...3...4...5...6...7...8...9...
DLOAD 2000 1. 1. 2001
RLOAD1 2001 2001 1111
$ Dynamic load at Grid 8373 (mechanical source) 1N
DAREA 2001 8373 3 1.0
$ Referenced Dynamic Load Tables
$ Constant Load Table TABLED1 1111
0. 1. 1000. 1. ENDT
$ METHOD CARD EIGENVALUE
$1...2...3...4...5...6...7...8...9...
$ Structure frequency range of interest EIGRL 50 -1.e-1 320.
$ Fluid frequency range of interest EIGRL 51 -1.e-1 320.
$
$ Frequency range
FREQ1 200 20.0 1.0 180
$1...2...3...4...5...6...7...8...9...
$ Damping coefficient for both structure and fluid
PARAM G 0.06
PARAM GFL 0.06
$
$ FLUID STRUCTURE PARAMETER
$1...2...3...4...5...6...7...8...9...
ACMODL DIFF BW
$
ENDDATA
Appendix B
Nastran input file for reciprocal calculation
$ MODAL FREQUENCY RESPONSE SOL 111
CEND
$
TITLE= FLUID-STRUCTURE-RESPONSE LABEL = Modal 0-320HZ
ECHO = NONE
$ Measuring points for all structure nodes
SET 1 = 4920 THRU 4935,5076,5111,5122,5133,5144,5155,5166,5177,5188, 5199,5210,5221,5228,5237,5246,5257,5268,5281,5293,5309,5481 THRU 5495, ...
...
33319 THRU 33329,33331 THRU 33341,36729 THRU 37419,37540 THRU 38151, 38272 THRU 38775,38896 THRU 39346,39467 THRU 39802,39923 THRU 40247, 40248
$
$ Structure output
VELOCITY(PUNCH,SORT1,REAL)=1 METHOD(STRUCT) = 50
METHOD(FLUID) = 51 FREQ = 200
$
$ Subcase for all ear position
$
SUBCASE 1 DLOAD = 1 SUBCASE 2 DLOAD = 2 ...
76
...
...
SUBCASE 41 DLOAD = 41 SUBCASE 42 DLOAD = 42
$
BEGIN BULK
$
$ Fluid and Structure meshes include ’FEM_all_coupled.bdf’
$ Absorbing boundary meshes include ’CAABSF.bdf’
$
$1...2...3...4...5...6...7...8...9...
PARAM AUTOSPC YES PARAM POST -1
$
$ Absorbing boundary conditions
$1...2...3...4...5...6...7...8...9...
PAABSF 10 210.8 210.8
$
$ Damping coefficient for both structure and fluid
$1...2...3...4...5...6...7...8...9...
PARAM G 0.06
PARAM GFL 0.06
$
$ Frequency range
$1...2...3...4...5...6...7...8...9...
FREQ 200 190.0
$
$ Fluid stucture parameter
$1...2...3...4...5...6...7...8...9...
ACMODL DIFF BW
$
$ Structure frequency range of interest EIGRL 50 -1.e-1 320.
$ Fluid frequency range of interest EIGRL 51 -1.e-1 320.
$
$ Acoustic source
$
$1...2...3...4...5...6...7...8...9...
ACSRCE 1 1001 1111 1.24 35836.
SLOAD 1001 767316 1.0
77
$1...2...3...4...5...6...7...8...9...
ACSRCE 2 1002 1111 1.24 35836.
SLOAD 1002 767400 1.0
...
...
...
$1...2...3...4...5...6...7...8...9...
ACSRCE 41 1041 1111 1.24 35836.
SLOAD 1041 763304 1.0
$1...2...3...4...5...6...7...8...9...
ACSRCE 42 1042 1111 1.24 35836.
SLOAD 1042 765478 1.0
$
$ quadratic function
$1...2...3...4...5...6...7...8...9...
$
TABLED4 1111 0.0 1.0 0.0 1.E6
0.0 0.0 0.0115 0.0 ENDT
ENDDATA
Appendix C
Matlab graphing programm
clear all; close all; clc;
freq=[];
%% read file
fname=’fsi_excit_fluid_plot’;
fpch=[fname,’.pch’];
display([’Processing file: ’,fpch]);
fid=fopen(fpch,’r’);
while 1
l=fgetl(fid);
if strncmp(l,’$FREQ’,5)
freq(end+1)=str2double(l(13:30));
end
if l==-1;break;end end
number_of_freqs=length(freq);
% read pch data frewind(fid);
c=textscan(fid,’%s’,’commentStyle’,’$’);
% process pch data entries_per_mp=21;
number_of_mp=length(c{1})/number_of_freqs/entries_per_mp;
cx=reshape(c{1},entries_per_mp,number_of_mp,number_of_freqs);
% Displacement Amplitude: 3:5 = real part, 13:15 = imag part uu=str2double(squeeze(cx([3:5,13:15],:,:)));
% absolute value of displacement or pressure abs_u(:,:)=sqrt(dot(uu,uu,1));
clf;
frewind(fid);
ID_C=zeros(number_of_mp,2);
i=1;
79
while i<=number_of_mp l=fgetl(fid);
if strncmp(l,’ ’,4)
ID_C(i,1)=sscanf(l(1:12),’%d’,1);
ID_C(i,2)=sum(abs_u(i,:));
i=i+1;
end
if l==-1;break;end end
fclose(fid);
%% read element file=’S18_S19.bdf’;
fid=fopen(file,’r’);
cqc=0;
disp([’=> Reading bulk data from ’, file]);
clear block_0;
[block_0]=fread(fid,’*char’).’; % read 100 000 000 characters into block_0 CQUADc=strfind(block_0,’CQUAD4’);
CQUAD_size=length(CQUADc);
CQUAD=zeros(CQUAD_size,5);
for m = 1:CQUAD_size
index = CQUADc(m);
cqc=cqc+1;
CQUAD(cqc,1) =sscanf(block_0(index+ 8:index+15),’%d’,1);
CQUAD(cqc,2) =sscanf(block_0(index+24:index+31),’%d’,1);
CQUAD(cqc,3) =sscanf(block_0(index+32:index+39),’%d’,1);
CQUAD(cqc,4) =sscanf(block_0(index+40:index+47),’%d’,1);
CQUAD(cqc,5) =sscanf(block_0(index+48:index+55),’%d’,1);
end
fclose(fid);
%% read nodes
[node,pos]=readGEOM12(’FEM_all_coupled.bdf’);
%% make plot ID=zeros(1,4);
X=zeros(1,4);
Y=zeros(1,4);
Z=zeros(1,4);
C=zeros(1,4);
hold on;
%for i=1:4000